I have been mostly been bouldering and I know there is a point at which you should stop using gear such as harnesses and quick draw webbing because it wears down with age. But I was wondering if after a certain number of years you should stop using rope?

According to Freedom of the Hills it depends on how often your rope gets used--

Daily - 1 year Weekends - 2 years Occasionally - 4 years

It also recommends replacement after a severe fall on a somewhat used rope. In my view these recommendations are very conservative; climbing ropes don't break unless they get exposed to battery acid or something.

I'll replace mine when it loses its stretchiness and generally looks and feels worn.

Sorry for the confusing wording, what I meant is that gear doesn't have a set expiration date and that the overriding factor is how much abuse it sees. If your storing it in a cool dry place out of the sun and not using it for long periods of time the useful life will not be affected. I would consider uv damage to be "use" since (unless we're talking about fixed ropes) it only occurs when you take the rope out to use it.

As an interesting perspective skydiving gear (mostly nylon) can be used for decades since it sees much less abrasion and even on a long day of jumping is exposed to the sun a mere fraction of the time that climbing gear is. I think the first rig I owned was about 17 years old when I got it and I'm pretty sure it's still being jumped years later.

I think the difference he is trying to point out is that if a rope is loaded linearly than the load is evenly distributed between all the fibers of a rope and can absorb a huge impact. Once you wrap it around a carabiner or make a bend to tie a knot it starts to load some fibers more than others causing failure at a lower load. The sharper the bend the more the strength is compromised. Of course if you load it over a sharp edge it would see more of a shear load and the edge would concentrate the force on a small portion of the rope greatly reducing the force required to cause failure.

there are ways to deal with cuts ... ie double/twins, extending protection, placing protection where it wont be loaded over an edge, edge protection, etc ... any old or new rope can get cut if you screw up

breaking .. well thats a total failure that should never happen realistically ...

But I was wondering if after a certain number of years you should stop using rope?

Depends on how often and how it is used. Also, how you store and how well you keep it clean. I can say at the current rate of which I use my rope and the care I give it, I probably have at least 5 years. For someone else, it could be very different.

Inspecting your rope regularly is important. Look for wear in the sheath and feel for spongy spots in the rope.

It doesn't depend on the age of the rope, rather than the condition of it. Too fuzzy, rigid, soft spots, severely glazed sheath, coreshot, ovalled out, etc are a good indication that you need to buy a new rope.